Does the online version have same functionality as desktop 2023 version for Mac?

No.  And You can't apply the Desktop CD/Download purchase to Online.  You have to pay for Online separately.  You will have to get a refund for the Desktop program.  Then you can use the Online web version.  Or try to upgrade your computer or find another computer to install it on.  The CD has both Windows and Mac programs on it.

Turbo Tax Refund request form

How do I request a refund for my TurboTax product?

Or Call in for a refund. When you fill out the from use the word BILLING ISSUES instead of the word “refund.

What is the Turbo Tax phone number

https://ttlc.intuit.com/turbotax-support/en-us/help-article/account-management/turbotax-phone-number/L0Od33nMQ_US_en_US

They might give you a service code to use the online version.

If you used the Desktop program last year here’s How to transfer into the Online version, expand the blue link if you used the CD/download last year

https://ttlc.intuit.com/community/entering-importing/help/how-do-i-transfer-last-year-s-return-into-turbotax-online/00/25953

If you used the Desktop program before you may notice several differences and not like the online version.  It has less features and no Forms Mode.  You can only do 1 return.  Your return is only saved online so be sure to save both the .tax2022 data file and the pdf file to your computer when you are done.  In case you need to amend in the future or if you need a copy to get a loan or something.  You might not be able to access your online return when you need a copy.

You cannot use the license code to pay for using online software.  The pricing is structured very differently.  So....you need to seek a refund for the CD/download---where did you purchase it?

And....just pay for online using a credit or debit card before you file.  It will ask you if you want to pay from your federal refund----if you say yes --- it will charge you an EXTRA fee of $40 ($45 in CA) for refund processing.

Online is.....different.  You do not have direct access to forms.  You get ONE return per fee, and pay separate fees for federal and state.  Your return is stored online in an online account.